Positive state controllability of positive linear systems

Guiver, Chris; Hodgson, David J.; Townley, Stuart

doi:10.1016/j.sysconle.2013.12.002

Cited by 14 publications

(30 citation statements)

References 17 publications

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“…Analogously, in regulating multiple outputs with multiple saturating inputs, we need to develop a different set of tools, described in the manuscript, and in particular draw upon recent positive state results in Guiver et al. ( 2014 ). Our results apply to situations outside of ecology, adding to their appeal, and are novel, although there are similarities to the results of Nersesov et al.…”

Section: Introductionmentioning

confidence: 99%

Robust set-point regulation for ecological models with multiple management goals

et al. 2015

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Population managers will often have to deal with problems of meeting multiple goals, for example, keeping at specific levels both the total population and population abundances in given stage-classes of a stratified population. In control engineering, such set-point regulation problems are commonly tackled using multi-input, multi-output proportional and integral (PI) feedback controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multi-objective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements, both described in the paper, and illustrate the theory with examples. Our results apply more generally to linear control systems with positive state variables, including a class of infinite-dimensional systems, and thus have broader appeal.

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Section: Introductionmentioning

confidence: 99%

Robust set-point regulation for ecological models with multiple management goals

et al. 2015

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“…On the other hand, new challenges also arise in the analysis and synthesis of positive systems, since traditional methods designed for general systems, though applicable, are often handicapped when dealing with such systems as they are not defined on linear spaces but a convex polyhedral cone. Therefore, new issues concerning the realization, reachability, and controllability of positive systems have been studied. Despite much attention has been devoted to studying reachability and realization of positive system, it is worth noting that approaches in designing positive observers have received increasing attention due to their practical significance …”

Section: Introductionmentioning

confidence: 99%

Descriptor state‐bounding observer design for positive Markov jump linear systems with sensor faults: Simultaneous state and faults estimation

Song

Lam

Chen

et al. 2020

Intl J Robust & Nonlinear

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Summary This article presents a descriptor observer design approach for positive Markov jump linear systems subject to interval parameter uncertainties and sensor faults. First, by taking the sensor fault term as an auxiliary state, an augmented descriptor system is constructed. A pair of positive observers with state‐bounding feature is then proposed, which enables simultaneous estimation of the system state and sensor faults. A necessary and sufficient condition on existence of the desired state‐bounding observer is derived by considering positivity and robust mean exponential stability of corresponding observer error dynamics. An iterative optimization algorithm is developed for the computation of the optimized observer matrices. Finally, a numerical example is presented to show the validity of the proposed methods.

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“…/ 2 R n is a nonnegative vector and without restrictions for the control vector u. / 2 R m , which is said to be positive state system according to Reference [10]. From now on, let us denote them by .A, B/ ps 0.…”

Section: Introductionmentioning

confidence: 99%

“…Differently from positive systems, only few authors have contributed to this emerging topic. It is worth mentioning Guiver et al [10] who dealt with the controllability property of these systems, which was termed positive state controllability. It is understood that .A, B/ ps 0 is positive state controllable in finite time if every nonnegative initial state x 0 can be transferred to any other nonnegative final state x f in a finite number of steps, and additionally, the nonnegativity of the states involved is maintained.…”

Section: Introductionmentioning

confidence: 99%

An algebraic approach to the structural properties of positive state control systems

Ricarte

Romero‐Vivó

2017

Math Methods in App Sciences

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In this paper, we deal with discrete‐time linear control systems in which the state is constrained to lie in the positive orthant independently of the inputs involved, that is, the inputs can take negative values. Such (positive state) systems appear, for example, in ecology models where the removal of individuals from a population is described. Controllability and reachability are fundamental properties of a system that show its ability to move in space, which are analyzed from an algebraic point of view throughout the text, paying special attention to the single‐input case. Copyright © 2017 John Wiley & Sons, Ltd.

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Positive state controllability of positive linear systems

Cited by 14 publications

References 17 publications

Robust set-point regulation for ecological models with multiple management goals

Robust set-point regulation for ecological models with multiple management goals

Descriptor state‐bounding observer design for positive Markov jump linear systems with sensor faults: Simultaneous state and faults estimation

An algebraic approach to the structural properties of positive state control systems

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